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Consumer Choice, Portfolio Decisions, and Transaction Costs

Edward Zabel

Abstract

The problem of the individual's consumption and portfolio choices over time has been the focus of recent studies by a number of authors. An attempt is made here to extend these results by examining the impact of transaction costs on optimal consumption and portfolio decisions. We are able to show that these costs considerably modify available results and greatly increase the difficulty of analyzing the consumer choice problem. The major reason is that now not only wealth, but also the composition of wealth, becomes important in the decision making process. To keep the exposition reasonably manageable we consider only a constant relative risk averse utility function and confine explicit attention to a two-period horizon. Since it is now necessary to examine portfolio choices in detail, we limit portfolio opportunities to a riskless asset, cash, and a risky asset, stock, with a random return. We assume proportional transaction cost for purchases or sales of stock. Wealth is taken to be the sum of cash and stock at the beginning of a period, while income is assumed to be zero, or included in initial wealth.